Never before in history has data been generated at such high volumes as it is today. Exploring and analyzing the vast volumes of data is becoming increasingly difficult. Information visualization and visual data mining can help to deal with the flood of information. The advantage of visual data exploration is that the user is directly involved in the data mining process. There are a large number of information visualization techniques which have been developed over the last decade to support the exploration of large data sets. In this paper, we propose a classification of information visualization and visual data mining techniques which is based on the data type to be visualized, the visualization technique, and the interaction and distortion technique. We exemplify the classification using a few examples, most of them referring to techniques and systems presented in this special section.

We propose a rudimentary taxonomy of interactive data visualization based on a triad of data analytic tasks: finding Gestalt, posing queries, and making comparisons. These tasks are supported by three classes of nteractive view manipulation: focusing, linking and arranging views. This discussion extends earlier work on the principles of focusing and linking and sets them on a firmer base. Next, we give a high-level introduction to a particular system for multivariate data visualization: XGobi. This introduction is not comprehensive but emphasizes XGobi tools that are examples of focusing, linking and arranging views, namely: high-dimensional projections, linked scatterplot brusing, and matrices of conditional plots.

AbstractÐVisualization techniques are ofincreasing importance in exploring and analyzing large amounts ofmultidimensional information. One important class of visualization techniques which is particularly interesting for visualizing very large multidimensional data sets is the class ofthe pixel-oriented techniques. The basic idea ofpixel-oriented visualization techniques is to represent as many data objects as possible on the screen at the same time by mapping each data value to a pixel ofthe screen and arranging the pixels adequately. A number of different pixel-oriented visualization techniques have been proposed in recent years and it has been shown that the techniques are useful for visual data exploration in a number of different application contexts. In this paper, we discuss a number ofissues which are ofhigh importance in developing pixel-oriented visualization techniques. The major goal ofthis article is to provide a formal basis of pixel-oriented visualization techniques and show that the design decisions in developing them can be seen as solutions ofwell-defined optimization problems. This is true for the mapping ofthe data values to colors, the arrangement ofpixels inside the subwindows, the shape ofthe subwindows, and the ordering ofthe dimension subwindows. The paper also discusses the design issues of special variants of pixel-oriented techniques for visualizing large spatial data sets. The optimization functions for the mentioned design decisions are important for the effectiveness of the resulting visualizations. We show this by evaluating the optimization functions and comparing it the results to the visualization obtained in a number of different application. Index TermsÐInformation visualization, visualizing large data sets, visualizing multidimensional and multivariate data, visual data exploration, visual data mining. 1

Visual data mining techniques have proven to be of high value in exploratory data analysis and they also have a high potential for mining large databases. In this article, we describe and evaluate a new visualization-based approach to mining large databases. The basic idea of our visual data mining techniques is to represent as many data items as possible on the screen at the same time by mapping each data value to a pixel of the screen and arranging the pixels adequately. The major goal of this article is to evaluate our visual data mining techniques and to compare them to other well-known visualization techniques for multidimensional data: the parallel coordinate and stick figure visualization techniques. For the evaluation of visual data mining techniques, in the first place the perception of properties of the data counts, and only in the second place the CPU time and the number of secondary storage accesses are important. In addition to testing the visualization techniques using re...

The grand tour and projection pursuit are two methods for exploring multivariate data. We show how to combine them into a dynamic graphical tool for exploratory data analysis, called a projection pursuit guided tour. This tool assists in clustering data when clusters are oddly shaped and in finding general low-dimensional structure in high dimensional, and in particular, sparse data. An example shows that the method, which is projection-based, can be quite powerful in situations which may cause methods based on kernel-smoothing grief. The projection pursuit guided tour is also useful for comparing and developing projection pursuit indices and illustrating some types of asymptotic results. 1 Introduction In this paper we show that two graphical methods for exploring high (say p) dimensional data, the grand tour (Asimov, 1985; Buja and Asimov, 1986), a dynamic tool, and projection pursuit (Kruskal, 1969; Friedman and Tukey, 1974; Huber, 1985), a static tool, naturally complement each o...

Scatterplots in 2D and 3D are very useful tools, but also suffer from a number of problems. Overplotting hides the true number of points that are displayed, and showing point clouds in 3D is problematic both in terms of perception and interaction. We propose a

We introduce an approach to visual analysis of multivariate data that integrates several methods from information visualization, exploratory data analysis (EDA), and geovisualization. The approach leverages the component-based architecture implemented in GeoVISTA Studio to construct a flexible, multiview, tightly (but generically) coordinated, EDA toolkit. This toolkit builds upon traditional ideas behind both small multiples and scatterplot matrices in three fundamental ways. First, we develop a general, MultiForm, Bivariate Matrix and a complementary MultiForm, Bivariate Small Multiple plot in which different bivariate repre- sentation forms can be used in combination. We demonstrate the flexibility of this approach with matrices and small multiples that depict multivariate data through combinations of: scatterplots, bivariate maps, and space-filling displays. Second, we apply a measure of conditional entropy to (a) identify variables from a high-dimensional data set that are likely to display interesting relationships and (b) generate a default order of these variables in the matrix or small multiple display. Third, we add conditioning, a kind of dynamic query/filtering in which supplementary (undisplayed) variables are used to constrain the view onto variables that are displayed. Conditioning allows the effects of one or more well understood variables to be removed from the analysis, making relationships among remaining variables easier to explore. We illustrate the individual and combined functionality enabled by this approach through application to analysis of cancer diagnosis and mortality data and their associated covariates and risk factors.

Never before in history has data been generated at such high volumes as it is today. Exploring and analyzing the vast volumes of data has become increasingly difficult. Information visualization and visual data mining can help to deal with the flood of information. The advantage of visual data exploration is that the user is directly involved in the data mining process. There are a large number of information visualization techniques that have been developed over the last two decades to support the exploration of large data sets. In this star report, we provide an overview of information visualization and visual data mining techniques, and illustrate them using a few examples.

An important goal of visualization technology is to support the exploration and analysis of very large amounts of data. In this paper, we describe a set of pixeloriented visualization techniques which use each pixel of the display to visualize one data value and therefore allow the visualization of the largest amount of data possible. Most of the techniques have been specifically designed for visualizing and querying large databases. The techniques may be divided into query-independent techniques which directly visualize the data (or a certain portion of it) and query-dependent techniques which visualize the data in the context of a specific query. Examples for the class of query-independent techniques are the screen-filling curve and recursive pattern techniques. The screen-filling curve techniques are based on the well-known Morton and Peano-Hilbert curve algorithms, and the recursive pattern technique is based on a generic recursive scheme which generalizes a wide range of pixel-ori...

D scatterplots are an extension of the ubiquitous 2D scatterplots that is conceptually simple, but so far proved hard to use in practice. But by combining them with a state-of-the-art volume rendering engine, multiple views, and interaction between these views, 3D scatterplots become usable and, in fact, useful. 3D scatterplots can not only show abstract data dimensions, but also the physical layout of points, and thus provide a link between feature space and the actual object. Brushing reveals connections between parts and features that otherwise are hard to find. This link also works not only from feature space to the spatial display, but also vice versa, which gives the user more freedom in exploring the data.